Traditional voltage references have utilized analog techniques to trim the output voltage of the reference to eliminate drift with temperature. This technique is referred to as "curvature compensation" and it appears widely in published literature. For example, such techniques are disclosed in Bang-Sup Song and Paul R. Gray, A Precision Curvature-Compensated CMOS Bandgap Reference, IEEE J. Solid State Circuits, Vol. SC-18, No. 6, December 1983 and C. R. Palmer and R. C. Dobkin, A Curvature-Corrected Micropower Voltage Reference, ISSCC Digest, February 1981. Both of these articles are incorporated herein by reference. In general, a bandgap reference is the conventional analog voltage reference that is utilized. This type of analog reference is made up of the sum of a bipolar device's base-emitter voltage, V.sub.bc, which has a negative temperature co-efficient and a thermal voltage, V.sub.th, which thermal voltage has a positive temperature co-efficient. The subtraction of the base-emitter voltages of two bipolar devices operating at different current densities will provide this thermal voltage. The values of V.sub.b and V.sub.th must be scaled appropriately to cancel out to first-order accuracy the temperature co-efficient of the entire circuit. To reduce temperature drift to even lower levels requires a second or third order compensation.
The primary disadvantage with respect to conventional temperature compensation techniques is that these operations are performed in the analog domain utilizing analog temperature curvature compensation techniques. The voltage V.sub.th is a linear voltage that is Proportional to Absolute Temperature (PTAT) wherein the base-emitter voltage is a polynomial which has some second and/or third order terms and therefore varies with temperature. When the voltage V.sub.bc is linearized with respect to temperature, the following equation results: EQU V.sub.OUT =V.sub.be +KV.sub.T +FV.sub.T.sup.2 +GV.sub.T.sup.3 +(1)
It can be seen that the constants K, F and G in Equation 1 are analog "real" number "quantities" as opposed to digital "integer" values. These quantities must be scaled and summed together such that the resultant voltage is insensitive to temperature changes. Since all scaling and summation is done in the analog domain, the circuits are highly sensitive to processing uncertainties and time drifts. Predominantly, laser trimmed resistors are utilized to adjust the temperature performance of the reference. Since the reference is packaged after the trimming is complete, post-calibration shifts are common due to piezo-electric effects caused by post-package stress.